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It was known that it could take several strokes using an axe to "get the job done". The most famous was the execution of Mary Stewart (Queen of Scots). Legend says it took three chops before the lady's head was fully separated from her body. Then she had the post-mortem indignity of her head dropping out of a wig and hitting the floor when they held it up by the hair to show it to the audience.

A really sharp sword handled by someone who knew how to use it was probably the "cleanest" tool till the invention of the guillotine. Still not as quick and certain as being blown into pink mist by a mortar round. But certainly better than how folks convicted of treason not of royal blood were disposed of. The second to last scenes of Braveheart forgot to include the still connected intestines roasting on hot embers and limb removal before decapitation.